How can I make hair that looks like it's flowing in water?
First, you need to check Hair Dynamics in the particle system settings.

You can reduce gravity in the Scene settings. If you set it to a positive number, the hairs will be attracted to the top, as if they were floating.

To add a more interesting movement, you can use one (or more) force field (Shift+A / Force Field). A Turbulence should give good results ; increase its Strength, Random and Flow values. Wind and Vortex can also be used to simulate water flow.

To make the setup step easier, you can specify a relative short animation range (like 1-100), and run the simulation (Alt+A). While the simulation is running, you can tweak the values of the force fields and see the result in live.